Cryogenic solid state heat pump

ABSTRACT

Systems and/or methods can provide for solid-state refrigeration below 1 degree Kelvin. By applying a simple sequence of ac electrical signals to a gated semiconductor device, electrons are cooled in a refrigeration sequence that, in turn, provides cooling directly to the heat load of interest. Electrons in a single subband of a semiconductor quantum well are expanded adiabatically into several subbands, resulting in a temperature drop. Repeated application of this cycle at MHz-GHz frequencies results in a significant cooling power. The anticipated cooling powers can compete with today&#39;s standard cryogenic system, the dilution refrigerator, which represents the market standard for achieving cryogenic temperatures.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a National State Entry of PCT InternationalPatent Application No. PCT/US2020/031082, filed May 1, 2020 entitled“Cryogenic Solid State Heat Pump,” which claims priority to and thebenefit of U.S. Provisional Application No. 62/841,542, filed May 1,2019 entitled “Cryogenic Solid State Heat Pump,” the disclosures ofwhich are all hereby incorporated by reference in their entireties.

STATEMENT OF FEDERALLY FUNDED RESEARCH OR SPONSORSHIP

This invention was made with government support under Grant No.NSF-DMR-0748856 awarded by the National Science Foundation. Thegovernment has certain rights in the invention.

BACKGROUND

Today's quantum computers are restricted in size and complexity by thecooling power of the dilution refrigerators that they require. Thedilution refrigerator is an extremely cumbersome piece of equipment withseveral mechanical pumps, pumping lines, and large tanks which can filla small room.

SUMMARY

According to certain aspects of the present disclosure, a device isprovided. The device includes a central reservoir configured to isolateelectrons. The device includes a first reservoir in communication withthe central reservoir. The device includes a second reservoir incommunication with the central reservoir. The electrons are isolated inthe central reservoir and expanded from a single subband state into amulti-subband state when the device is selectively operated at a firststage. Heat from the first reservoir is exchanged with the centralreservoir when the device operates a second stage responsive to thedevice operating at the first stage. The electrons are isolated andcompressed in the central reservoir from the multi-subband state to thesingle subband state when the device is selectively operated at a thirdstage subsequent to the heat being exchanged between the first reservoirand the central reservoir. Excess heat in the central reservoirgenerated during the second stage is ejected into the second reservoirwhen the device operates at a fourth stage responsive to the deviceoperating at the third stage.

According to certain aspects of the present disclosure, a method isprovided. The method includes selectively operating a device at a firststage to isolate electrons in a central reservoir and expand theelectrons from a single subband state into a multi-subband state. Themethod includes exchanging heat from the first reservoir to the centralreservoir when the device operates at a second stage responsive to thedevice operating at the first stage. The method includes selectivelyoperating the device at a third stage, subsequent to the second stage,to isolate the electrons in the central reservoir and compress theelectrons in the central reservoir from the multi-subband state to thesingle subband state. The method includes ejecting excess heat in thecentral reservoir, generated during the third stage, into the secondreservoir when the device operates at a fourth stage responsive to thedevice operating at the third stage.

According to certain aspects of the present disclosure, a device isprovided. The device includes a central reservoir configured to isolateelectrons. The device includes a first reservoir in communication withthe central reservoir. The device includes a second reservoir incommunication with the central reservoir. The electrons are isolated inthe central reservoir and expanded from a single subband state into atriple subband state when the device is selectively operated at a firststage. Heat from the first reservoir is exchanged with the centralreservoir when the device operates a second stage responsive to thedevice operating at the first stage. The electrons are isolated andcompressed in the central reservoir from the triple-valley state to thesingle valley state when the device is selectively operated at a thirdstage subsequent to the heat being exchanged between the first reservoirand the central reservoir. Excess heat in the central reservoirgenerated during the second stage is ejected into the second reservoirwhen the device operates at a fourth stage responsive to the deviceoperating at the third stage.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 illustrates an example cryogenic solid state heat pump device.

FIG. 2 illustrates an example process for operating the examplecryogenic solid state heat pump device of FIG. 1 .

DESCRIPTION

Systems and methods are described for thermoelectric cooling atcryogenic temperatures, e.g., from 250 mK down to 1 mK, using electronsin a standard transistor structure as the refrigerant “gas” that isalternately expanded and compressed in a Carnot cycle to induce cooling.A thermoelectric mechanism relies on adiabatic expansion from a singlesubband into multiple subbands, in one instance into the so-called“valley” degree of freedom in quantum wells. This idea is introduced bythe PI in this proposal and can be demonstrated experimentally. In someexamples, the systems and methods can provide a factor-of-3 cooling intemperature per refrigeration cycle, and cascaded realizations of thesame device may achieve over two orders of magnitude in thermal cooing.

The systems and methods can improve cryogenic refrigeration, replacingcumbersome room-filling dilution refrigerators with simple on-chiprefrigerators, and allow cryogenic research to advance without furtherdepleting rare helium gas reserves.

Helium is a necessary natural resource for cryogenic research, but theworld helium reserves are projected to drop by 30% in the next 7 years,while demand from the medical MRI & semiconductor processing industry isexpected only to increase. See, e.g., W. P. Halperin, Nature Phys. 10,467 (2014), The impact of helium shortages on basic research. As aconsequence, the low-temperature research required for investigatingquantum computation and quantum materials will suffer greatly,preventing advance into the quantum information age. The systems andmethods can provide a new cryogenic refrigeration technology whichallows research to proceed independently of the world helium supply.

The systems and methods can create a semiconductor heat pump usingadiabatic expansion of electrons in a central region to extract heatfrom one reservoir, and then use adiabatic compression to eject heat tothe opposite reservoir (See FIG. 1 ).

FIG. 1 illustrates an example cryogenic solid state heat pump device 10,as depicted in stages 100, 200, 300, 400. The device 10 can include athin layer of hot electrons (red) and cold electrons (blue) with thecentral electron reservoir 12 serving as a heat pump. The Carnot cyclestarts, at the stage 100 (e.g., step #1), with electrons in the centralisolated region 12 expanded into a multi-subband degeneracy state tocool them. Heat is then extracted from the right reservoir 14 as itequilibrates with the center region 12, at stage 200 (e.g., step #2),after which the central region 12 is isolated again and compressed, asillustrated at the stage 300 (e.g., step #3). The excess heat can now beejected into the left hot reservoir 16, at stage 400 (e.g., step #4).The central region 12 is isolated and the Carnot cycle begins again.

A first aspect of the device 10 includes the “expansion” in this Carnotcycle, which does not physically expand the electron layer 18, butincreases the number of degrees of freedom by a factor of the number ofsubbands by applying a gate voltage. These degrees of freedom in oneinstance are called “valleys,” a common feature in industrysemiconductors such as silicon, germanium, and aluminum arsenide. Thesecond aspect includes the cyclic nature of the cooling. Previous theoryconsidered only single-shot cooling (e.g., L. G. C. Rego and G.Kircenow, Appl. Phys. Lett. 75, 2262 (1999), Electrostatic mechanism forcooling semiconductor heterostructures), whereas the device cancontinuously cool by running the Carnot cycle at MHz frequencies.

In the present realization, a 2D layer of aluminum arsenide grown on the(111) plane can be used to tune the electrons from a single subband totriple-subband occupancy, thereby cooling the electron temperature by afactor of 3 from T₁ to T₂=⅓T₁. Repeated application of this cycle cancool an entire semiconductor chip, and a multistage cooler with N stagescan cool by N factors of ⅓ to T₂=⅓NT₁. A starting temperature of T₁=250mK may be used since it is readily achievable with a simple closed-cycle³He refrigerator, and the cascaded-stage refrigerator can cool down to 1mK. This technology can make cumbersome room-filling dilutionrefrigerators obsolete, replaced by a cooling element with dimensions5×5×0.5 mm3.

The device 10 can contain a reservoir of electrons in a thin layercalled a quantum well 18. The electrons occupy the lowest energy stateof the quantum well 18, called the lowest subband. This reservoir isdesigned so that small changes in the electrostatic confinement cancause higher subband(s) to lower their energy, thereby allowing theelectron gas to adiabatically “expand” into these subbands 20, loweringtheir temperature. By connecting these cooled electrons to a thermalload and isolating them again before “compressing” the electrons back toa single subband, a heat pump cycle 500 (e.g., the stages 100, 200) isdefined which can be repeated at high frequencies to induce a largeamount of cooling power.

The cooling principle in use is a cyclic adiabatic expansion of atwo-dimensional electron gas inside of a semiconductor quantum well. Thesubband expansion device consists of a quantum well 18 in asemiconductor with an additional subband or subbands whose energy can betuned both above and below the Fermi energy by of order ˜kT, where k isthe Boltzman constant, and T is the hot-side operating temperature, inthis case around T=1 K. A capacitive gate over the cooling reservoirwill tune the subband energies from above to below the Fermi energy(cooling step) and from below to above the Fermi energy (heating step)with set of tunable electrostatic gates that alternately couple to theneighboring heat load for the cooling step and to the heat sink for theheating step. One candidate semiconductor for this implementation is analuminum arsenide AlAs quantum well which is slightly miscut from thenominal crystal axis. This semiconductor contains multiple valleys, andthe miscut angle slightly imbalances the energy of those valleys so thatan electrostatic gate can the relative energies of these valleys toinduce the refrigeration effect described above.

Quantum wells can be grown according to the above. These structures canbe tuned from single subband occupancy to multi-subband occupancy withapplication of a gate voltage, verified with the quantum Hall effect. Alow-temperature thermometer may be fabricated with low-costpre-amplifiers so that absolute temperatures can be deduced from thethermal noise. The electron heat pump can be tested by making a thinnedsample with front-gates, back-gates, and throttle gates as shown in FIG.1 .

FIG. 2 illustrates an example process 2000 for operating the exampledevice 10 of FIG. 1 . While FIG. 2 is described with reference to FIG. 1, it should be noted that the process steps of FIG. 2 may be performedby other systems.

The process 2000 begins by proceeding to step 2010 where the device 10is selectively operated at the first stage 100 to isolate electrons in acentral reservoir (e.g., the central isolated region 12) and expand theelectrons from a single subband state into a multi-subband state. Asillustrated at step 2012, the device 10 operates at the second stage 200to exchange heat from a first reservoir (e.g., the right reservoir 14)to the central reservoir. The device 10 is selectively operated at thethird stage 300, subsequent to the second stage, to isolate theelectrons in the central reservoir and compress the electrons in thecentral reservoir from the multi-subband state to the single subbandstate, as depicted at step 2014. As illustrated at step 2016, the deviceoperates at the fourth stage 400 to eject heat in the central reservoir,that was generated during the third stage 300, into a second reservoir(e.g., the left reservoir 16) when the device 10 operates at the fourthstage 400 responsive to the device 10 operating at the third stage 300.As illustrated by the return arrow, the process can then proceed back tostep 2010.

Applications of the systems, methods and devices may include, but arenot limited to, quantum computation at temperatures below T<0.1 K tooperate, and/or laboratory research on the fundamental properties ofmaterials and quantum phenomena at major research labs and universitiesthroughout the world which may require the lowest possible cryogenictemperatures.

Advantages may include, but are not limited to, cooling powers exceeding500 uW at 100 mK, small chip to yield an equivalent amount of coolingpower, greatly simplifying the refrigeration process and providingenough cooling power for scalable quantum computers to finally be built,and/or an all-electrical solid-state cooling mechanism, robust againstthe typical failure modes of the dilution refrigerator, namely gasleaks, gas contamination, clogged flow lines, leaky heat exchangers,etc.

While various embodiments have been described, it can be apparent thatmany more embodiments and implementations are possible. Accordingly, theembodiments are not to be restricted.

I claim:
 1. A device, comprising: a central reservoir configured toisolate electrons; a first reservoir in communication with the centralreservoir; and a second reservoir in communication with the centralreservoir, wherein the electrons are isolated in the central reservoirand expanded from a single subband state into a multi-subband state whenthe device is selectively operated at a first stage, wherein heat fromthe first reservoir is exchanged with the central reservoir when thedevice operates a second stage responsive to the device operating at thefirst stage, wherein the electrons are isolated and compressed in thecentral reservoir from the multi-subband state to the single subbandstate when the device is selectively operated at a third stagesubsequent to the heat being exchanged between the first reservoir andthe central reservoir, and wherein excess heat in the central reservoirgenerated during the second stage is ejected into the second reservoirwhen the device operates at a fourth stage responsive to the deviceoperating at the third stage.
 2. The device of claim 1, wherein thedevice is configured to cyclically operate between the first stage andthe fourth stage.
 3. The device of claim 1, wherein the device operatesat frequencies in the Megahertz (MHz) range.
 4. The device of claim 1,wherein the device comprises a dimension in a range of 5 millimeters by5 millimeters by 0.5 millimeters.
 5. The device of claim 1, wherein theelectrons include a first temperature when the first stage begins andinclude a second temperature when the first stage ends.
 6. The device ofclaim 5, wherein the second temperature is one third of the firsttemperature.
 7. The device of claim 1, further comprising a gateassociated with the second reservoir wherein a voltage is applied to thegate to selectively operate the device at the first stage.
 8. The deviceof claim 1, wherein the device comprises a layer formed of aluminumarsenide.
 9. The device of claim 8, wherein the layer formed of aluminumarsenide comprises a miscut angle.
 10. The device of claim 1, furthercomprising a cold load in communication with the first reservoir. 11.The device of claim 1, further comprising a heat sink in communicationwith the second reservoir.
 12. A method, comprising: selectivelyoperating a device at a first stage to isolate electrons in a centralreservoir and expand the electrons from a single subband state into amulti-subband state, wherein the central reservoir is in communicationwith a first reservoir; exchanging heat from the first reservoir to thecentral reservoir when the device operates at a second stage responsiveto the device operating at the first stage; selectively operating thedevice at a third stage, subsequent to the second stage, to isolate theelectrons in the central reservoir and compress the electrons in thecentral reservoir from the multi-subband state to the single subbandstate, wherein the central reservoir is in communication with a secondreservoir; and ejecting excess heat in the central reservoir, generatedduring the third stage, into the second reservoir when the deviceoperates at a fourth stage responsive to the device operating at thethird stage.
 13. The method of claim 12, further comprising: cyclicallyoperating the device between the first stage and the fourth stage. 14.The method of claim 12, wherein the device operates at frequencies inthe Megahertz (MHz) range.
 15. The method of claim 12, wherein thedevice comprises a dimension in a range of 5 millimeters by 5millimeters by 0.5 millimeters.
 16. The method of claim 12, wherein theelectrons include a first temperature when the first stage begins andinclude a second temperature when the first stage ends.
 17. The methodof claim 16, wherein the second temperature is one third of the firsttemperature.
 18. The method of claim 12, wherein the device comprises alayer formed of aluminum arsenide.
 19. The method of claim 18, whereinthe layer formed of aluminum arsenide comprises a miscut angle.
 20. Adevice, comprising: a central reservoir configured to isolate electrons;a first reservoir in communication with the central reservoir; and asecond reservoir in communication with the central reservoir, whereinthe electrons are isolated in the central reservoir and expanded from asingle-valley state into a triple-valley state when the device isselectively operated at a first stage, wherein heat from the firstreservoir is exchanged with the central reservoir when the deviceoperates a second stage responsive to the device operating at the firststage, wherein the electrons are isolated and compressed in the centralreservoir from the triple-valley state to the single valley state whenthe device is selectively operated at a third stage subsequent to theheat being exchanged between the first reservoir and the centralreservoir, and wherein excess heat in the central reservoir generatedduring the second stage is ejected into the second reservoir when thedevice operates at a fourth stage responsive to the device operating atthe third stage.